What is the algebraic formula for the distance of the diagonal of a cube?

Answer 1

s√3 where s is the length of an edge.

First, the diagonal of a face is (df)^2 = s^2 + s^2
or (df)^2 = 2s^2 and df = √2s
Then, the diagonal of the cube is a hyponenuse of a right triangle with lengths s and √2s
So (dc)^2 = s^2 + (√2s)^2 = 3s^2
and dc = s√3

Answer 2

Let the cube be situated at the origin so that we are working only with positive axes.
Let x be the side of the cube.
Then, the distance of the diagonal is the distance from the origin (0,0,0) to (x,x,x)
The distance, call it d, or length of the diagonal is then (kinda like Pythagorean theorem):
d=sqr(x^2 + x^2 + x^2) = sqr(3x^2) = xsqr(3)

Answer 3

you can find this by placing a cube in 3 space with one vertex on the origin... the diagonal would be vector coming from this vertex with the value the length of a vector is given by
sqrt(x^2+y^2+z^2)
in this case it would be
sqrt(L^2+W^2+H^2)

since its a cube all sides are 1
sqrt(1^2+1^2+1^2)
sqrt(3)

Answer 4

when a cubes side dimension is A, then the diagonal dimension is
D = sq.root{A^2 + A^2 + A^2} = A sq.root{3} = 1.73 A

Answer 5

If the length of a side is x, then the answer is

SQRT(x^2 + x^2 + x^2)

= SQRT(3x^2)

= (SQRT3)*x

Answer 6

d^2=3*s^2
d=s√3

Answer 7

Use vectors. The vector from (0,0,0) to (1,1,1) has length
sqrt(3), right.

Answer 8

if the edge is x long:

sqrt(3x^2)